How is this a synecdoche: "Take thy face hence."? What does this quote mean: "When to the sessions of sweet silent thought..."?

A synecdoche is a part of speech in which one word or term is used to describe another word or term in the other's place.

In the command, "Take thy face hence," the speaker is not telling the person at whom it's commanded to take just their face to a different location, they're saying that they want someone to go somewhere else altogether.

The word "face" is used to refer to the addressee's entire body. The sentence could instead read "Take thyself hence," commanding that someone move not just their face, but their entire person.

As such, the synecdoche arises in the use of the word "face" to refer to someone's entire body.

The line you've quoted is from a Shakespearean sonnet. The line makes more sense within context, so here are the first 3 lines of the sonnet (Sonnet 30):

When to the sessions of sweet silent thought
I summon up remembrance of things past,
I sigh the lack of many a thing I sought...

A "session" is just a period of time. The speaker is commenting that they frequently get lost spending time in "sweet silent thought," during which they remember things that have happened to them ("remembrance of things past") and become sad thinking about things they wanted, but never got ("I sigh the lack of many a thing I sought").

So, the line "When to the sessions of sweet silent thought" is just the speaker's introduction to their discussion on the personal time they spend contemplating and reflecting on their past.